Local Reaching Centrality (Mones, Vicsek & Vicsek 2012)

Local reaching centrality measures how much of the network is reachable from a node.

Usage

centrality_reaching_local(x, mode = "all", ...)

Arguments

x: Network input (matrix, igraph, network, cograph_network, tna object).
mode: For directed networks: "all" (default), "in", or "out".
...: Additional arguments passed to centrality.

Value

Named numeric vector of local reaching centrality values.

Details

Directed unweighted: \(LRC(v) = |\{u : u \ne v, v \to u\}| / (N - 1)\).
Undirected unweighted: average of \(1/d(v, u)\) over all \(u \ne v\), divided by \(N - 1\). Numerically equal to igraph::harmonic_centrality(normalized = TRUE).
Weighted: NetworkX convention, where edge weights are interpreted as strengths and path length is \(\sum_e (\mathrm{total\_weight} / w_e)\). Per-path score is the mean of original edge weights along the shortest path.

Bit-exact match against networkx.local_reaching_centrality across all three branches. Bit-exact match against igraph::harmonic_centrality(normalized = TRUE) for the undirected unweighted branch. See reaching_global for the graph-level hierarchy measure derived from per-node LRC.

References

Mones, E., Vicsek, L., & Vicsek, T. (2012). Hierarchy measure for complex networks. PLoS ONE, 7(3), e33799.

Examples

# Directed path A -> B -> C
adj <- matrix(c(0,1,0, 0,0,1, 0,0,0), 3, 3, byrow = TRUE)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_reaching_local(adj, mode = "out")
#>   A   B   C 
#> 1.0 0.5 0.0